Consider the square of the derivative operator D². a) Show that D² is a linear operator. b) What is the eigenfunctions and corresponding eigenvalues of D2. c) Give an example of an eigenfunction of D2 which is not an eigenfunction of D.

Help with d please

a.) The function, f(x) = 3X2-1, is an eigenfunction of the operator, (see image attched). Find the eigenvalue corresponding to this eigenfunction. b.) Show that the function is an eigenfunction of the operator, (See image attached) and calculate the eigenvalue.

2. Show that the wavefunction (eigenfunction) of a state a) can be expressed in position basis as (x/a).

What are the Eigenspace and Eigenvalues of B

Help with part a please

Consider the linear system X1 = and Find the eigenvalues and eigenvectors for the coefficient matrix. A₂ = 0 JI ← A, V₁ 9 V2 = 81 = = -3 6 - - 4 x. help (numbers) help (matrices) help (numbers) help (matrices) For each eigenpair in the previous part, form a solution of a' = Ax. Use t as the independent variable in your answers.

please,don't provide handwriting solution...

b) 3 -2 Given matrix A = -2 6 2. Suppose the eigenvalues of A and the bases for the A=1-/²2 2 corresponding A₁ = -2, Ex=-2 4 eigenspaces are as follows 2-((-)) and 2 ---(Q)-()} 2 and X₂ = 7, Ex=7 i. Explain why A is orthogonally diagonalizable. ii. Give the relation between Ex=-2 and Ex-7. Hence, find an orthogonal matrix Q that diagonalizes matrix A and the corresponding diagonal matrix D such that D = Q-¹AQ. iii. Hence, calculate A².

Show that v= (7) Is an eigenvector of the matrix: A = -29 35 - 20 26 and find the corresponding eigenvector.